Questions tagged [complex-networks]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
3 votes
1 answer
234 views

What are the right mathematical tools / language to analyse complex networks over time?

In this article about human physiology as a complex network the authors say that: "Lacking adequate analytic tools and a theoretical framework to probe interactions within and among diverse ...
user avatar
2 votes
0 answers
80 views

Derivation of a series expansion

I am trying to derive the critical coupling strength for synchronisation in a network of phase oscillators with noisy input. I am following the steps outlined in Sakaguchi, Hidetsugu. "...
user avatar
1 vote
0 answers
43 views

Is a function of a centrality measure a centrality measure?

I have been trying to wrap my head around the following question. Suppose you a have a centrality measure for a weighted, undirected network. Let's call the calculated centralities with $\pmb{x}>0$....
user avatar
1 vote
2 answers
94 views

Which infinite random graphs with percolation threshold $p_c=0$ are transient?

I am interested in long-range percolation models with heavy-tailed degree distributions such as DHH13, GLM21, Y6. The simplest example is scale-free percolation in which vertices are elements $\mathbb{...
user avatar
0 votes
0 answers
21 views

Weighted network centrality measure

I am looking for some references (I could not find much online) and/or technical guidance on the eigenvector centrality. More specifically on its generalization for a weighted network, i.e. how to ...
user avatar
2 votes
0 answers
402 views

what is the computational complexity of Louvain algorithm?

I am not able to find out the computational complexity of the Louvain Algorithm. Can anyone here help me? link of the paper given below: DOI: 10.1088/1742-5468/2008/10/P10008 https://doi.org/10.1038/...
user avatar
  • 21
2 votes
1 answer
305 views

Random subgraph properties

Consider a graph $G$ of $N$ vertices and $M$ edges, and assume $G$ has typical complex network properties: it is not necessarily connected, but it has a high clustering coefficient and a giant ...
user avatar
2 votes
0 answers
125 views

How much algebra is preferable for studying/doing research in dynamical/complex system and networks

I asked this question earlier on Mathematics StackExchange (link), but I think it might be better to put it here. This question seems quite broad to ask... The situation here is that I'm a second-...
user avatar
  • 121
2 votes
0 answers
134 views

The topological complexity of polytopes

Polytopes arise naturally when modelling fundamental structures in Biology such as RNA and proteins [1,2]. Recently, it occurred to me that a complexity measure on the topology of polytopes might be ...
user avatar
  • 3,263
1 vote
0 answers
219 views

Research-level blogs on complex networks:

I'm an applied mathematician that has a research interest in complex networks for modelling biological systems and I wondered whether the MathOverflow community might know of research-level blogs that ...
2 votes
1 answer
3k views

Adjacency definition for a directed graph

For an undirected graph, we know that nodes are adjacent to each other if there is a link that connects them. What about adjacency for directed graphs? Is it based on: outgoing links: node $n$ is ...
user avatar